Ash isn't doing this for fun, he's put himself through many trials and hardships that'd test anyone's resolve, and make most people give up and quit (which people in the anime have done). It can be competitive, but we humans compete for fun. Being a Master is just that - you've mastered that vocation.
So is his goal just misguided? Does he not realize what Champions already do? That being a Trainer is about raising the next generation to be better people who treat their Pokemon better than the previous? He's not doing this because he wants the impossible either, as there have been many challenges and tests he's failed, yet never reattempted. He has no role-model or someone who inspired him to want to achieve this, because no one has ever been the all-time No.1 Master before.
Why does Ash want to become the world's greatest Pokemon Master so badly? He has no desire for fame or fortune - so it really begs the question.
